**Step 1 — Write the given data.**
$$r = 42 \text{ cm}, \qquad \theta = 30^\circ, \qquad \pi = \frac{22}{7}$$

**Step 2 — Formula for the area of a sector.**
$$A = \frac{\theta}{360^\circ} \times \pi r^2$$

**Step 3 — Substitute for the minor sector.**
$$A_{\text{minor}} = \frac{30}{360} \times \frac{22}{7} \times 42 \times 42$$

**Step 4 — Simplify.**
$$= \frac{1}{12} \times \frac{22}{7} \times 1764 = \frac{1}{12} \times 22 \times 252 = \frac{5544}{12} = 462 \text{ cm}^2$$

**Step 5 — Find the area of the whole circle.**
$$A_{\text{circle}} = \pi r^2 = \frac{22}{7} \times 1764 = 5544 \text{ cm}^2$$

**Step 6 — Find the major sector.**
$$A_{\text{major}} = A_{\text{circle}} - A_{\text{minor}} = 5544 - 462 = 5082 \text{ cm}^2$$

$$\boxed{\text{Minor sector} = 462 \text{ cm}^2,\qquad \text{Major sector} = 5082 \text{ cm}^2}$$